Related papers: A dispersion function for the regularized kappa di…
Plasma technology has found widespread applications in numerous domains, yet the techniques to manipulate plasma transport predominantly rely on magnetic control. In this review, we present a streamlined diffusion-migration method to…
Recently, there emerges different versions of beta function and hypergeometric functions containing extra parameters. Gaining enlightenment from these ideas, we will first introduce a new extension of generalized hypergeometric function and…
Nowadays many real-world datasets can be considered as functional, in the sense that the processes which generate them are continuous. A fundamental property of this type of data is that in theory they belong to an infinite-dimensional…
We establish a connection between anomalous heat conduction and anomalous diffusion in one dimensional systems. It is shown that if the mean square of the displacement of the particle is $<\Delta x^2> =2Dt^{\alpha} (0<\alpha\le 2)$, then…
In this paper, we derive the expression for spectral dimension using a modified diffusion equation in the kappa-deformed space-time. We start with the Beltrami-Laplace operator in the kappa-Minkowski space-time and obtain the deformed…
This paper deals with the solution of unified fractional reaction-diffusion systems. The results are obtained in compact and elegant forms in terms of Mittag-Leffler functions and generalized Mittag-Leffler functions, which are suitable for…
Fluctuations in conjugate thermodynamic variables are studied using the cross-correlation function. A new procedure is given enabling the derivation of fluctuation formulas for a system in equilibrium. Specifically, the cross-correlation…
Dawson's integral and related functions in mathematical physics that include the complex error function (Faddeeva's integral), Fried-Conte (plasma dispersion) function, (Jackson) function, Fresnel function and Gordeyev's integral are…
We discuss conditions for the enhancement of fusion reactivities arising from different choices of energy distribution functions for the reactants. The key element for potential gains in fusion reactivity is identified in the functional…
The eigenvalue probability density functions of the classical random matrix ensembles have a well known analogy with the one component log-gas at the special couplings \beta = 1,2 and 4. It has been known for some time that there is an…
Modelling diffusion processes in heterogeneous media requires addressing inherent discontinuities across interfaces, where specific conditions are to be met. These challenges fall under the purview of Mathematical Analysis as…
In this paper we have criticized the so-called Landau damping theory. We have analyzed solutions of the standard dispersion equations for longitudinal (electric) and transversal (electromagnetic and electron) waves in half-infinite slab of…
A novel 3-D higher-order finite-difference time-domain framework with complex frequency-shifted perfectly matched layer for the modeling of wave propagation in cold plasma is presented. Second- and fourth-order spatial approximations are…
We extend an isothermal thermal model of ultracold neutral plasma expansion to systems without spherical symmetry, and use this model to interpret new fluorescence measurements on these plasmas. By assuming a self-similar expansion, it is…
A general formulation of translationally invariant, parametrically correlated random matrix ensembles, is used to classify universality in correlation functions. Surprisingly, the range of possible physical systems is bounded, and can be…
We consider a thermal particle which is diffusing in velocity-space and in a weakly confining potential characterized by the inverse hyperbolic sine function of the particle velocity $v$ and the control parameter $v_c$. The stationary state…
The propagation of microwaves across a turbulent plasma density layer is investigated with full-wave simulations. To properly represent a fusion edge-plasma, drift-wave turbulence is considered based on the Hasegawa-Wakatani model.…
Synchrotron emission and absorption determine the observational appearance of many astronomical systems. In this paper, we describe a numerical scheme for calculating synchrotron emissivities and absorptivities in all four Stokes parameters…
We recently introduced the recursive divisor function $\kappa_x(n)$, a recursive analogue of the usual divisor function. Here we calculate its Dirichlet series, which is ${\zeta(s-x)}/(2 - \zeta(s))$. We show that $\kappa_x(n)$ is related…
We apply expansion methods to obtain an approximate expression in terms of elementary functions for the space and time dependence of wave packets in a dispersive medium. The specific application to pulses in a cold plasma is considered in…